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Determinants of the CDS

Spreads of Japanese Firms

Before and After the Global

Financial Crisis

Koichi Iwai

DP 2011-2

August, 2011

The views expressed in this paper are those of the authors and do not necessarily reflect the views of the

Financial Services Agency or the FSA Institute.

<FSA Institute Discussion Paper Series DP2011-2 (2, 2011)>

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Determinants of the CDS Spreads of Japanese Firms

Before and After the Global Financial Crisis

Koichi IWAI*

Abstract

The global financial crisis has led to even greater interest in credit default swap (CDS) markets. CDS

markets are regarded as one of the underlying causes in the financial crisis, and given the circumstances

that regulatory reviews have been progressed, rigorously examining price formation in CDS markets

before and after the crisis would be important for considering the functions of the CDS market and how

future regulation ought to be. Nevertheless, only a limited understanding of price formation in the

Japanese CDS market has been accumulated so far. The aim of this paper is to empirically verify the

determinants of CDS spreads whose reference entities are Japanese non-financial corporations. I regard

as the possible determinants of CDS spreads both the structural variables and some state variables which

capture overall market trends and macroeconomic development. Analyses in this paper succeed to find

several characteristics of price formation in the CDS market, including some phenomena never reported

before. First, structural variables satisfy the sign condition and are generally significant, but they cannot

fully explain the fluctuation of CDS spreads. Even if market- and macro-related variables are included

in addition to the structural variables as the independent variables, the explanatory power of the model

is generally low. It is arguable that the so-called “credit spread puzzle” exists in the Japanese CDS

market as well. Second, a phenomenon not reported in foreign countries is confirmed, namely, that the

explanatory power of the regression model improves after the financial crisis. A possible reason for this

is that, after the onset of the financial crisis, market fluctuations in foreign countries begin to have a

considerable impact on the Japanese CDS market. Third, it seems that some unobservable systemic

factors become main factors for CDS spreads variations after the financial crisis. These findings will

help to understand the price formation mechanisms in the Japanese CDS market.

Keywords: Credit default swaps (CDSs), Structural model, Dynamic Heterogeneous Panel Model

* Research Fellow, FSA Institute, Financial Services Agency. I would like to acknowledge Professor Akira Kohsaka of

Osaka University and Professor Naoyuki Yoshino of Keio University for the valuable feedback they provided on the

earlier drafts of this paper. This paper represents the personal opinion of the author and is not the official view of the

Financial Services Agency or FSA Institute. Any possible errors in the paper are entirely the responsibility of the author.


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1. Introduction

The appraisal of credit default swaps (CDSs) changed considerably with the onset of the global

financial crisis in 2007. Prior to the financial crisis, it seemed to be blindly believed that CDS markets

lead to improvements in social welfare through improving the efficiency of resource allocation and

lessening the financial restrictions on households and business. Since various transactions, including

short selling, could be conducted with very small transaction costs in the CDS markets, investors with

diverse trading motives, such as hedging or speculation, are supposed to participate in the markets,

which could lead to more active information production and more efficient price discovery on the

reference entities. Nevertheless, after the onset of the financial crisis, attention began to shift to negative

views, including that CDS markets had amplified the systemic risk of the entire financial system and

that they had lowered social welfare by provoking moral hazard and excessive risk taking in the banking

sector. Furthermore, financial authorities show concern over unfair trading in CDS markets whereas

several incidents of insider trading extending into CDS markets and stock markets occurred in some

countries. Regulators in advanced countries began to examine measures for tightening the regulation

against CDS markets, and some of them have already been implemented.1

Amid rising concern over CDS markets, empirical examinations on the functions and price

formation in U.S. and European CDS markets have been advanced. The determinants of CDS spreads

and the price discovery among CDS markets, bond markets, stock markets, and other related markets

are designated as key research topics. In contrast, as for the Japanese CDS market, empirical

investigations have been limited so far, so the characteristics of price formation are little understood. In

particular, no empirical research has been reported on the CDS spreads of non-financial firms in Japan.

Unlike CDSs in which a financial institution or the Japanese government is the reference entity, most

CDS transactions of non-financial corporations are conducted domestically. Therefore, it is preferable

that non-financial corporations are included in assessing price formation in the Japanese CDS market. In

this paper, I will focus my attention on Japanese non-financial corporations, and will examine the

determinants of their CDS spreads and the characteristics of price formation before and after the

financial crisis.

The rest of this paper is structured as follows. In Chapter 2, I review previous studies and summarize

the main aims of this paper. Chapter 3 explains the empirical method used in this paper. As the possible

determinants of CDS spreads, I incorporate not only the structural variables but also a number of state

variables, such as interest rates and others that indicate stock market trends. Chapter 4 shows the results

of empirical analyses. I examine the validity of the structural model and discuss the significance of the

1 Positive views about CDS markets can be found in Hellwig (1994), Allen and Gale (2006), Hakenes and Schnabel

(2008), and Aschcraft and Santos (2009). Conversely, negative views have been detailed by Partnoy and Skeel (2007),

Brunnermeier (2008), Hellwig (2008), and Hakenes and Schnabel (2009). For the regulations pertaining to CDS markets

and details of recent changes, refer to BIS (2008) and IOSCO (2009).


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state variables. I also turn my attention to the differences and characteristics before and after the recent

financial crisis. In Chapter 5, I draw my conclusions.

2. Previous literature

One of the widely accepted theoretical models on the determinants of credit risk is known as the

structural model or structural approach.2 Structural models usually define a firm’s value as a stochastic

process, regard the situation where the firm value falls below a certain threshold (debt value) as default,

and calculate the frequency (probability) of such a situation occurring based on option pricing theories.

In a simplest structural model, the credit risk of a firm can be determined by three structural variables:

leverage, volatility of firm values and the risk-free interest rate. Credit risk can be expressed as an

increasing function of leverage and the volatility, and a decreasing function of risk-free interest rate.3 A

number of empirical studies have been carried out with regard to this theoretical conclusion: To what

extent can the levels and fluctuations of credit spreads be explained by the three structural variables? If

structural variables cannot fully explain the variation of credit spreads, what mechanisms are driving the

credit spreads’ fluctuation?

While a number of previous studies on bond spreads have confirmed that the structural variables

satisfy the theoretical sign conditions, it has also been reported that the explanatory power of the

structural models is generally low. This low explanatory power is often called the “credit spread puzzle.”

For example, Collin-Dufresne et al. (2001) investigate the determinants of bond spreads in the U.S.

using a linear model in which structural variables are the explanatory variables, and report that the R2

remains generally around 0.2 to 0.3. Faced with the credit spread puzzle, researchers have focused on

other factors that might affect credit risk besides structural variables, such as taxes, liquidity risk and

other systemic risks.4 However, the mechanisms and variables by which fluctuations in credit risk can

be explained with a sufficiently high degree of accuracy are yet to be discovered at the present point in

time.

Recently, there has been another stream of studies examining the determinants of credit risk, that is,

analyses of CDS markets. In evaluating credit risk, CDS spreads could be better indicators than bond

spreads for a number of reasons.5 Longstaff et al. (2005) report that the majority of CDS spreads can be

2 Merton (1974), Black and Cox (1976), Longstaff and Schwarz (1995), Collin-Dufresne and Goldstein (2001), etc.

Ammann (2001) describes various structural models. 3 Depending on the assumptions of the model, it is possible that a positive relationship can occur between the risk-free

interest rate and the credit risk (see, Longstaff and Schwartz (1995) for example). However, our discussion will consider

that the structural model “assumes a negative relationship between the risk-free interest rate and the credit risk” for

simplicity of explanation,. 4 See, Elton et al. (2001) and Driessen (2005), for example. 5 Two main reasons have been suggested. First is that CDS spreads are less arbitrary than bond spreads: the level of bond

spreads changes depending on what is used for the benchmark (risk-free interest rate) while CDS spreads are calculated

as the premium for a notional principal amount and no benchmark-related problems occur. Second, short selling on bond

markets is quite difficult in reality, whereas in the CDS markets short sales can be conducted relatively easily. For this


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explained using firm-specific bankruptcy risks. Ericsson et al. (2009) focus on structural models, and

investigate the determinants of the changes of CDS spreads. They report that: (i) the estimated

parameters of the structural variables are consistent with theory; (ii) the lower the credit-rating, the

greater the absolute value of the parameters; (iii) while the R2 is about 0.6 in the case of levels

regression, it is around 0.2 in the case of difference regression. Blanco et al. (2005) also measure the

effects of structural variables on CDS spreads while their focus is on comparing price discovery in the

U.S. bond market and CDS market. They indicate that the explanatory power of the model measured by

R2 is low, at about 0.25, while signs of coefficients are in accordance with the theory. Di Cesare and

Guazzarotti (2010) study the CDSs of U.S. non-financial firms before and after the global financial

crisis. They direct their attention not only to structural variables but also to various market variables,

such as stock price returns, difference between long-term and short-term interest rates, corporate bond

spreads, the U.S. VIX index, and the theoretical value of CDS spreads. They report: (i) about half of all

fluctuations in CDS spreads can be explained using their explanatory variables, and the explanatory

power is higher than existing research; (ii) significant difference in the explanatory power of the model

before and after the financial crisis cannot be detected; (iii) CDS spreads of many issuers increased

simultaneously during the crisis situation, which implies that some common factors have influence on

the CDS market.

Studies on the determinants of credit risk for Japanese firms include Ito and Harada (2004), Baba

and Inada (2009), Ooyama and Sugimoto (2007), Shirasu and Yonezawa (2007), Inaba (2007),

Nakashima and Saito (2009), and Ooyama and Hongo (2010). Of these, Ooyama and Sugimoto (2007),

Shirasu and Yonezawa (2007), and Nakashima and Saito (2009) are few who analyze non-financial

corporations. Ooyama and Sugimoto (2007) use OLS estimation to examine the determinants of bond

spread changes, and report that: (i) although a negative relationship is often observed between the risk-

free interest rate and bond spread, positive relationships also occur for some issuers; (ii) an increase in

swaption volatility, which is supposed to represent the uncertainty of interest rates in the future,

coincides with the increase in the bond spread; (iii) bond spreads seem to have no clear relationship with

the stock price index return and the volatility thereof; (iv) R2 is at a low level, which implies that some

other factors not incorporated into the estimation model might cause changes in the bond spread.

Shirasu and Yonezawa (2007) take the effects of the economic environment and liquidity factor into

account as possible determinants of bond spread in addition to the intrinsic attributes of individual

issues. Although the focus of their analysis is on investigating the presence of the “flight to quality” and

“flight to liquidity” phenomena, we can confirm the following from the analyses described in the paper:

(i) the signs of coefficients on the structural variables are different to those expected in the structural

model for some firms; (ii) overall stock market trends and bond spreads are inversely correlated; (iii)

contrary to theoretical inference, the difference of the risk-free interest rate has a positive effect on bond

spreads. Nakashima and Saito (2009) propose to examine the determinants of bond spreads based on an

reason, it is expected that the evaluations of credit risk by market participants will be reflected more accurately in CDS

markets.


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estimation model in which time dummies and other factors are added to the structural model. They

report that (i) estimates of the structural variables are consistent with the structural model, (ii) overall

trends in financial markets affect bond spreads as stock price returns and change of bond spreads have a

significant negative relationship. By comparing these existing studies on bond spreads, we can confirm

that there are differences in the sign and significance of the parameter estimates for structural variables

and other state variables.

There are many studies on the Japanese CDS market, but most of those are about CDSs whose

reference entity is a major financial institution. Ito and Harada (2004) suggest that CDS spreads are an

effective indicator capturing the credit risk of major banks. Inaba (2007) employs a structural model to

examine the determinants of CDS spreads for three major banks. He adopts structural variables,

swaption volatility and other variables as determinants of CDS spreads, and reports that the CDS

spreads of major banks are determined consistently with the structural model and the spreads are also

affected by the macro economy, such as by business trends. Baba and Inada (2009) explore the

determinants of subordinated debt spreads and CDS spreads of four major banks, and further investigate

the price discovery between the two spreads. They report that CDS spreads negatively react to stock

price returns, and are positively related to the Japanese sovereign CDS spreads and the historical

volatility of CDS spreads.

As shown above, previous studies on the credit risk of Japanese firms have been accumulated

primarily around bonds and CDSs of financial institutions. As far as I know, no empirical research that

investigates CDSs of non-financial firms has been reported so far. As mentioned earlier, in view of the

limitations inherent in bond spreads, we should be wary about relying on the results of bond market

analyses alone for examining the determinants of credit risk. Therefore, I will focus on the CDS

transactions of non-financial corporations and examine their determinants. Specifically, I will clarify the

extent to which actual fluctuations of CDS spreads can be accounted for by structural variables, and

then will look at the mechanisms that can explain the part which cannot be captured by structural

variables. Furthermore, I will compare the price formations of before and after the recent financial crisis.

3. Methodology

3.1. Selection of variables

Table 1 shows the list of variables in this study. Although no commonly acknowledged definition of

the credit risk variable has been established in existing research, four different definitions — level value

of credit risk spreads, level difference, logarithmic level value, and logarithmic difference — are often

used.6 Therefore, this paper will discuss the results of empirical analyses using these four definitions —

6 The studies by Ericsson et al. (2009), Ooyama and Hongo (2010), Nakashima and Saito (2009), Duffee (1998), Collin-

Dufresne et al. (2001), Di Cesare and Guazzarotti (2010), Greatrex (2008), Ooyama and Sugimoto (2007), Alexopoulou

et al. (2009), and Gai et al. (2009) utilize level values and the differences thereof. In contrast, Edwards (1984), Das et al.

(2009), and Forte (2009) suggest that logarithmic level values are theoretically better. Inaba (2007) uses logarithmic level


- 6 -

defined as , , , and respectively — in so far as the explanation does

not become complicated.

Explanatory variables are comprised of structural variables and other state variables. The structural

variables are leverage ( ), firm value volatility ( and the risk-free interest rate

( ). In calculating , periodic financial data are transformed to daily data using linear

interpolation.7 Firm value and its volatility cannot be observed directly in market places. Existing

studies often use one of three proxy variables: volatility derived from option pricing theory, historical

volatility, and GARCH-type volatility. In this paper, an option-based volatility measure that is

calculated in accordance with the procedure outlined in the Appendix is selected.8 Furthermore it is not

necessarily evident which interest rate should be used for the risk-free interest rate. Most existing papers

use either the yields on long-term government bonds or long-term swap rates. Similar to Ericsson et al.

(2009) and others, I will use the ten-year government bonds yield as risk-free interest rate ( ).9 As the

treatment in many of previous papers, I add the square of the risk-free interest rate, ( ), as an

explanatory variable. Readers should note that “structural variables” do not include the square of the

risk-free interest rate in the explanation below.

Since the credit spread puzzle was acknowledged, variables expressing the macro environment and

market trends have been adopted as the possible determinants of credit risk. These variables could be

construed as state variables for grasping the term structure of interest rates, the stochastic variation of

firm values, the time-varying recovery rate and so forth. However, because the rigorous mathematical

relation between these variables and credit risk has not been explicitly derived in most theoretical

models, the questions of which indicators to be incorporated into the estimation model and how to

incorporate them have to be left to the discretion of researchers.10

I select the following variables that

have been used frequently in existing studies as independent variables that capture the macro

values in order to stabilize the variance of the dependent variable. Forte and Peña (2009) and Ferrucci (2003) utilize

logarithmic differences. 7 In empirical analyses of credit risk, it is normal to use linearly interpolated financial data. For example, Collin-Dufresne

et al. (2001), Greatrex (2008), Ericsson et al. (2009), Nakashima and Saito (2009), and Ooyama and Hongo (2010) utilize

linear interpolation technique. 8 Analyses are also conducted using the GARCH volatility (based on GARCH (1,1) model) and the historical volatility

(90-day) of stock price returns as the proxy variable for firm value volatility. The outcomes are virtually the same as the

findings in this paper. Thus, the claims made in this paper would also hold true for other proxy indexes for firm value

volatility. 9 Forte and Lovreta (2009) remark that it would be inappropriate to use the swap interest rate as a proxy variable for the

risk-free interest rate during the recent financial crisis situation. 10 For example, with regard to the positioning of state variables in structural models, the leading study examining the

determinants of CDS spreads, Collin-Dufresne et al. (2001), only goes as far as presenting the relational expression CS(t)

= CS(Vt, rt, [Xt]), where CS is credit spread, V is firm value, r is the swap rate, X is a variety of state variables, and t is

time. But recently, using variables that grasp macroeconomic trends and overall market trends in credit risk evaluation

models in an ad hoc fashion has become fairly widespread. At the same time, statistically evaluating the effects of these

variables on credit risk has also been advanced. For example, Sommar and Shahnazarian (2009) take a statistical

approach in examining the effects of industrial production, commodity prices and short-term interest rates on credit risk;

and Simons and Rolwes (2009) take a similar approach in examining the effects of GDP, interest rates, foreign exchange,

equity returns and the fluctuations thereof, as well as crude oil prices on credit risk. Chau-Lau (2006) presents a summary

of statistical attempts that incorporate macro factors in a credit risk model.


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environment and market trends: , the difference between long-term and short-term interest

rates ( ), return on the domestic stock market ( ), the logarithmic market capitalization

( ), swaption volatility ( ), and U.S. VIX index ( ).11

Additional explanations are necessary for some variables. As discussed in detail by Di Cesare and

Guazzarotti (2010), the difference between long-term and short-term interest rates could have either a

positive or negative effect on credit risk spread. Considering this ambiguity, I regard as a control

variable in this paper. There is also uncertainty surrounding the interpretation of stock market returns.

Blanco et al. (2005) is among the scholars who view a stock market return as a proxy variable for

default recovery rates; but it could also be thought of as a state variable grasping macro environment

trends. Although the return on individual stocks could possibly be added as an explanatory variable, I

have not adopted it in this paper because it could have a high correlation with leverage and market

capitalization. Logarithmic market capitalization is generally used as an indicator for firm size. If firm

size correlates with trading volume in the CDS market, we could also regard as a proxy of

liquidity. Meanwhile, gathering necessary data to evaluate the overall liquidity of the Japanese CDS

market and the liquidity of individual CDS issues is difficult, so I have positioned as a control

variable for liquidity concurrently with firm size. Swaption volatility could be regarded as an indicator

capturing fluctuations of the risk-free interest rate and the uncertainty over future prospects of the

interest rate environment. U.S. VIX index has been construed in previous studies as a proxy that reflects

the uncertainty of the overall U.S. stock market as well as global event risk. No matter which

interpretation is adopted, can be regarded as an instability factor in overseas markets from the

perspective of the Japanese CDS market or Japanese investors.

3.2. Estimation model

Many previous studies use the linear model of equation (1).

　

K

ktitkikiiti xSpread

1,,,,,

）（1

Spreadi,t is the variable representing the credit risk of firm i at time t, and

are used separately as this variable. xi,k,t is the kth

explanatory variable of firm i at time t, and

the explanatory variables (k=1,2,…,K) are comprised of structural variables and other state variables as

mentioned in the previous section. εi,t is the error term of firm i at time t. Previous research can be

divided broadly depending on whether equation (1) is perceived as a time series model of each

individual firm or it is treated as panel data. Collin-Dufresne et al. (2001), Ericsson et al. (2009) and

Ooyama and Sugimoto (2007) are among those who use the OLS method to estimate equation (1) for

each firm. Inaba (2007) also makes estimates for each individual firm, but uses the maximum likelihood

method in which a moving average (MA) process is assumed in εt. In contrast, Di Cesare and

11 When selecting non-structural variables, I referred to Collin-Dufresne et al. (2001), Blanco et al. (2005), Pan and

Singleton (2006), Inaba (2007), Ooyama and Sugimoto (2007), Greatrex (2008), Ericsson et al. (2009), Nakashima and

Saito (2009), and Di Cesare and Guazzarotti (2010).


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Guazzarotti (2010), Baum and Wan (2010) use pooled OLS, fixed-effect models and random-effect

models. In addition, Nakashima and Saito (2009) use an instrumental variable fixed-effect model which

takes into account the endogeneity of credit risk spread and leverage, whereas Ötker-Robe and Podpiera

(2010) use a dynamic panel model. Most studies that use panel analysis impose a constraint that the

parameters excluding constant terms are homogenous for all i. If the true parameters are homogenous,

estimating time series models for each firm will lead to loss in efficiency. On the other hand, it is known

that imposing homogeneity in parameters in the panel model will result in biased estimators in cases

where the parameters are heterogeneous in the true model.12

Using the dynamic heterogeneous panel (DHP) model is one possible solution to these problems.

The DHP model is a model that allows parameters to differ in cross-section. Ferrucci (2003),

Alexopoulou et al. (2009), and Gai et al. (2009) use the DHP model in their empirical analysis of credit

risk. Following these previous attempts, this paper estimates a DHP model whose exact formulation is

derived as follows. First, I suppose that credit spread (Spread) follows the autoregressive distributed lag

model (ARDL (p, q1, …, qk)) as shown in equation (2).

p

j

q

jitijtiijjtiijit XSpreadSpread

1 0,

',

）（2

Xit is a K×1 vector composed of the explanatory variables while δij is the K×1 vector of the parameters

and λij is a constant parameter. μi is the fixed effect specific to i, and εit is the error term. The

explanatory variables include structural variables and other state variables. Reparameterization of

equation (2) will produce the following error-correction representation:

1

1

1

0,

*,

*'1,

p

j

q

jitijtiijjtiijititiiit XSpreadXSpreadSpread

）（3

where

q

jmim

*ij

p

jmim

*ij

q

j

K

kikiji

p

jiji

)q,...,,j(

),p,...,,j(,/,

1

10 11

121

12111

　　

　　　　

Inside the brackets of equation (3) is an expression that represents the long-run equilibrium. θi is called

the long-run parameter. ϕi is a parameter that captures how fast the divergence is adjusted if the credit

risk spread diverges from the long-run equilibrium level. In this paper, ϕi is called the adjustment

parameter. If the adjustment parameter is negative and significant, the divergence converges toward the

long-run equilibrium even if it occurs in the short run. The second and third terms on the right-hand side

are the parts which reflect the short-term movements of the dependent variable. Throughout this paper,

this is called the short-run adjustment equation. Pesaran et al. (1999) propose a pooled mean group

(PMG) model, in which θi in equation (3) is common to all i, but which permits other parameters to be

heterogeneous, and they derive the maximum likelihood estimator. Pesaran and Smith (1995) and

12 See Pesaran and Smith (1995), Pesaran and Shin (1998), Pesaran et al. (1999), etc.


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Pesaran et al. (1999) propose another estimator, called the mean group (MG) estimator. In this model, θi

is also thought to differ for each i, and so equation (2) is estimated for each i, and then the mean value

of those estimates is calculated. Selection between the PMG model and MG model can be made by the

Hausman test. In this paper, following Alexopoulou et al. (2009) and Gai et al. (2009), I will focus on

an ARDL(1,1,…,1) model with an imposed lag of one period.13

The DHP model is useful in the analysis of financial asset prices which generally follow the I(1)

process, and could be a suitable method when investigating an equilibrium mechanism. There are four

reasons for this. First, the DHP model will produce a consistent and asymptotic normal estimator even if

stationary variables and the I(1) process are mixed together in the model.14

Second is the fact that the

DHP model explicitly analyzes long-run equilibrium relationships. This means that, if a divergence

from the long-run equilibrium relationship occurs, we can examine whether there is a force working to

restore the equilibrium. Thirdly, using the DHP model, we can also analyze how the dependent variable

responds to changes in explanatory variables in the short term. Moreover, the DHP model allows

different short-term responses for each individual. Fourth, the DHP model can also be applied to data

sets with small N but large T sample.

In view of the above discussion, both a time series model using OLS and a DHP model will be

analyzed in this paper. I will report the results of OLS using the four variables as the dependent variable

— , , , and — in order to directly compare the results with the

previous studies. With regard to the DHP model, I will estimate models in which and

are used as the dependent variable.

4. Empirical results

4.1. Descriptive statistics

The sample in this paper covers the CDS transactions where the reference entities are 45 non-

financial firms whose daily data are continuously available for the period from 1 April 2004 to 30

September 2009 (Table 2). Table 2 also shows the list of the reference entities and credit-rating class of

the companies. The sample consists of several sectors; the manufacturing industry accounts for about

half of the sample, with the remainder being such industry sectors as trading companies, real estate,

utilities, and consumer finance. Viewed by the credit-rating, the sample data are distributed across each

class of rating, with main focus on investment-grades.

Table 3 shows several basis statistics. Looking at the correlation between the CDS level variables

and the explanatory variables, we can confirm some characteristics that are consistent with the

13 To be precise, in this paper, I will use an ARDL (1,…,1) model and a model in which parameter constraints are

imposed on the short-run adjustment equation and long-run equilibrium equation in the ARDL (1,…,1) model. A DHP

model in which parameter constraints are imposed on an ARDL model can be seen in Martinez-Zarzoso and Bengochea-

Morancho (2004), Alexopoulou et al. (2009), and Gai et al. (2009). 14 However, certain conditions need to be satisfied, such as T being adequately long. For further details, see the

references listed in footnote 12.


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theoretical conclusions of the structural model and with existing empirical results. Furthermore, the

maximum absolute value of correlation coefficients is about 0.6, so a multicollinearity is unlikely to be

a serious concern. Table 3-(3) shows the results of the DF-GLS and PP tests of unit roots. ,

, , , and can be confirmed to be the I(1) process for almost

all firms. The results of the unit root tests show that regression analyses using the level variables may

lead to the problem of spurious regression.

4.2. Time series model

Table 4 and Table 5 show the OLS results using the level variable and the difference variable

respectively. 15

The “coef” and “s.e.” in the Tables are the cross-section mean values of the parameter

estimates and standard errors respectively. In contrast, the “t-value” and “p-value” are the t-value and p-

value pertaining to the constant term from the OLS estimation, in which the dependent variable consist

of the parameter estimates derived from OLS regressions for each firm while the explanatory variable is

a constant term.16

In cases where only structural variables are used as explanatory variables (hereafter “base model”),

in almost all formulations, the results are in line with the structural model, regardless of whether the

variables are level variables or difference variables. In other words, estimated coefficients of

and are positive and significant,17

and the coefficient of is negative and

significant, except for one case. In terms of the validity of models, adj-R2 is less than 0.04 for the model

using the difference variables whereas it is relatively high at more than 0.6 for the model using the level

variables.

In addition to structural variables, I select other explanatory variables that are indicative of market

trends. Analyses are separated into two types; one including and the other without it. The model

without is a formulation that considers domestic factors only. In contrast, the model including

can be regarded as the one which takes overseas factors into account. To begin with, looking at the

estimation results of the level variables, we can confirm the following characteristics. First, similar to

the results of the base model mentioned above, the signs of coefficients for structural variables are

consistent with the structural model. However, coefficients of and are insignificant in a

number of specifications. Second, the coefficients of take an opposite sign depending on whether the

left-hand side variable is logarithmic form or not. As mentioned earlier, although parameters for

15 Following Inaba (2007), I re-estimated the model reported below using the maximum likelihood method, assuming

ARMA (1,1) for the error term. Since mostly similar results are obtained, only the results of the OLS estimation are

reported below. 16 To be precise, the t-value (p-value) is the t-value (p-value) for the null hypothesis that the parameter of the constant

term is zero. This approach of using OLS estimates is a simplified method for understanding whether the each

explanatory variable is significant across cross-section. Same method is used in cases where there are a large number of

cross-sectional samples. Collin-Dufresne et al. (2001) and Blanco et al. (2005), for instance, adopt this method for their

empirical analyses of credit risk spreads. Similar methods will be used when reporting the results of the PMG model. 17 In this paper, the significance of hypothesis testing is basically assessed at the 1% level. Therefore, such expressions as

“is significant (is not significant)” refer to assessments at the 1% level, unless otherwise noted.


- 11 -

could theoretically be either positive or negative, the fact that the sign changes depending on the form of

the dependent variable is difficult to understand economically. It is expected that this results might be

due to non-stationarity of the variables. Third, the estimated parameters for are positive and

significant in all cases. If we regard as a proxy variable for recovery rate, this result would mean

that an increase in recovery rate leads to an increase in credit risk. The finding that overall stock market

trends have a positive effect on the credit risk spreads of individual firms can also be found in Ooyama

and Sugimoto (2007) and Pynnӧnen et al. (2004), but the reasoning given in these previous studies has

not necessarily been well defined. Fourth, in the model where is used as the dependent variable,

the coefficients for become negative. This result is different from Ooyama and Sugimoto

(2007) and Inaba (2007). Fifth, the coefficients for are positive, indicating the possibility that the

impact of any uncertainty in the U.S. stock market could reach to the Japanese CDS market. Finally,

adj-R2 are relatively high, at about 0.7 to 0.9.

In contrast, looking at the estimation results for the difference variable being used as a dependent

variable, the following points are noted. First, although the coefficients’ sign of the structural variables

are no different to the results of the level variables, statistical significance of some variables changes;

most of the coefficients of turn to be significant whereas the coefficients of lose

significance in the formulation on which is used as the dependent variable. In the same

formulations, none of the parameters of , , or are significant, suggesting

that interest rate movements do not have any effect on . This finding differs from Nakashima and

Saito (2009) who report a statistically significant relationship between credit risk spreads and interest

rates. The second feature is that intuitively easy-to-understand results are obtained; the coefficients of

and are negative and positive respectively in all cases. Third, the coefficients of

are positive and significant, which is similar to the results for the level variables. Fourth, the adj-

R2 rise no higher than 0.03 to 0.07, which is lower than those reported in previous studies on the U.S.

market. The adj-R2 calculated by Blanco et al. (2005) and Ericsson et al. (2009) using weekly data are

about 0.15 to 0.25. Studies that use monthly data, such as Di Cesare and Guazzarotti (2010), Collin-

Dufresne et al. (2001), and Greatrex (2008), report adj-R2 from 0.3 to 0.5. After re-estimating the model

in Table 5 using monthly data (monthly mean values), the adj-R2 are calculated at around 0.3 to 0.4.

Although the differences in explanatory variables and specifications of the models render it impossible

to make simple comparisons, the above results seem to show that the explanatory power of the models

in this paper is, at best, at a similar level as the empirical results of other countries.

4.3. Dynamic heterogeneous panel (DHP) model

The findings in section 4.2 indicate that regression analyses using level variables as the dependent

variable could lead to the problem of spurious regression, and the estimations based on difference

variables lead to the issue of the poor explanatory power. In contrast, as mentioned earlier, one of the

features of the DHP model is that it does not require variables to be stationary. The DHP model can

incorporate the information reflected in both level and differenced variables through the long-run


- 12 -

equilibrium equation and the short-run adjustment equation. Accordingly, we could overcome the above

problems if we use the DHP model.

To begin with I estimate models in which structural variables are the only independent variables, and

then will move to models including other state variables as additional explanatory variables. The actual

estimation model is equation (3) which is a variation of the ARDL model. Because is an indicator

that captures trends in overseas markets, it would not be regarded as a variable that determines the long-

run equilibrium value of CDS spreads for Japanese corporations. Therefore, I regard it as an exogenous

variable and only consider its effects via the short-run adjustment equation. Table 6 shows the

estimation results. Irrespective of the form of dependent variable, the PMG model is selected as a result

of the Hausman test (1% level). Consequently, I will report only the results of the PMG models.

Before expanding on the features of the estimation results, an explanation needs to be given as to the

figures in the Tables. The figures for the long-run equilibrium equation in the PMG model report the

parameters that are common to all i. In other words, the “coef”, “s.e.”, “z-value”, and “p-value” in the

Tables can be interpreted in the same way as ordinal regression analyses. In contrast, with respect to

each of the variables in the short-run adjustment equation, the parameters are permitted to be different

between individual reference entities. The “coef” in the Tables relating to these heterogeneous

parameters is the cross-sectional average of the estimated coefficients. The reported “s.e.”, “z-value”,

and “p-value” of these variables are the standard error, z-values, and p-values relating to the constant

term in the OLS estimation, in which the parameter estimates of each issue are the dependent variables

while a constant term is the only explanatory variable. “χ(p-value)” are test statistics and associated p-

value of the null hypothesis that the parameters are common to each issue. The adj-R2 in the lower part

of the Tables is the cross-sectional average of adj-R2.

Panel A and Panel B in Table 6 report the results of the PMG models where and

are used as a dependent variable respectively. The signs of coefficients in the long-run equilibrium

equation are, on the whole, consistent with the structural model and previous studies. Meanwhile, three

variables among the explanatory variables in the short-run adjustment equation — , , and

— have not been used much as explanatory variables in existing literature. In addition, it

would be hard to think of any economic significance these variables would have on CDS spreads.

Thereupon, I decide to re-estimate the DHP model with zero restrictions imposed on the parameters of

these three variables, and examine the results in detail below.18

The estimation results of the restricted model are shown in Table 7. I estimate two models just as

with Table 6; one including and the other without . The PMG models are selected as a result of

the Hausman test in all cases, and so only the results of the PMG models are reported. The following

features of the estimation results are worthy of attention. First, the coefficients of the structural variables

18 As we could not observe any great difference between the estimation results in Table 6 and Table 7, whether

restrictions are imposed upon , , has no great bearing on the sign or significance of the parameters

of the other explanatory variables. For this reason, the basic assertions below hold true regardless of whether there are

restrictions or not.


- 13 -

both in the long-run equilibrium equation and in the short-run adjustment equation have the same signs

as those suggested by the structural model, and moreover, most of the coefficients are significant.

Consequently, the price formation mechanism suggested by the structural model is considered to be at

work. Second, the coefficients of , , and in the long-run equilibrium equation are

significant in all cases. Furthermore, considering the fact that the adjustment parameter is significantly

negative, there is a strong possibility that an equilibrium relationship has formed between

( ) and the variables contained in the long-run equilibrium equation. This result also suggests

limitations of the structural model, in the sense that the structural variables alone are not enough to

explain the equilibrium levels of CDS spreads. In addition, the speed of adjustment towards a long-run

equilibrium is supposed to be different for each CDS since the null hypothesis that the adjustment

parameters are the same for all issues can be rejected. Third is the finding that the parameters of

are significantly positive. Also, the adj-R2 increase considerably by adding to the explanatory

variables. In the estimation of the time series model, and are significant, but it is not

confirmed that adding these variables to the independent variables would cause a considerable increase

in the adj-R2. These results of the PMG model show that the U.S. market trends and perhaps global

event risks have a strong effect over the Japanese CDS market in the short term. However, the level of

the adj-R2 per se could hardly be called high compared to previous studies, and in this sense I would

have to say that the credit spread puzzle exists in Japan too.

As described in footnote 8, the results thus far generally hold true even if we change the definition of

firm value volatility. I will now, however, confirm the robustness of the results from a different

perspective. Specifically, I will use the distance-to-default indicator ( ) as an explanatory variable in

place of three structural variables. As evident from the process for deriving this indicator outlined in the

Appendix, this measure can be thought of as a variable that aggregates the information contained in

three structural variables.19

If this measure reflects credit risk accurately and investors are acting

rationally, the parameters of should be negative and significant. Looking at the estimation results in

Table 8, in all but one case, the signs of coefficients pertaining to are negative, and in most cases,

they are significant. However, positive and significant results can also be seen in the formulation in

which is used as the dependent variable. The fact that the negative and significant result could

not be obtained consistently throughout might suggest that either the structural model providing the

theoretical basis for does not indicate true credit risk, or that investors are not acting rationally in

accordance with the structural model.20

Although we need to be mindful of this point, the estimation

results using confirm the adjustment parameter to be negative and significant, and so there seems to

be a strong possibility that a long-run equilibrium relationship exists between CDS spreads and

19 See Vassalou and Xing (2004), Byström (2006), Das et al. (2009), Bharath and Shumway (2008), and Du and Suo

(2007). 20 This is a composite hypothesis that commonly occurs when examining market efficiency. It is difficult to clarify which

of the two hypotheses is rejected.


- 14 -

explanatory variables. Moreover, we could reconfirm such phenomena as an improved adj-R2 by adding

variable in the model.

4.4. Before and after the financial crisis

4.4.1. DHP model

The recent global financial crisis has resulted in attention being switched to more negative

perceptions of CDS markets than positive views. Some authors, such as Di Cesare and Guazzarotti

(2010) and the IMF (2009), note that price formation in CDS markets has changed after the financial

crisis. In the rest of this section, I examine whether the financial crisis prompted a change in the price

formation in CDS spreads in Japan. Dividing the sample into before and after the financial crisis, I will

examine the differences in estimated coefficients. Following the discussion of Di Cesare and

Guazzarotti (2010), I regard the financial crisis happened July 2007. I designate the period from April 1,

2004 through to June 29, 2007 as the pre-crisis period; and the period from July 1, 2007 through to

September 30, 2009 as the crisis period.21

Different formulations in section 4.3 are also conducted, but

since no major differences are found, only the results on the model that includes will be discussed

for the rest of this section.

Table 9 shows the estimation results. Regardless of whether or is used as a

dependent variable, some common features can be identified. First, the significance of individual

variables is more apparent and the overall fitness of the model is better in the second half. Although

some variables in the long-run equilibrium equation and in the short-run adjustment equation are not

significant in the first half, almost all variables are significant in the second half. Furthermore the adj-R2

in the second half is clearly higher than that in the first half. Second, the possibility of stronger

interconnection between CDS markets and bond markets/stock markets can be observed in the second

half. For example, coefficients on interest rate related variables in the second half clearly differ from

those in the first half. In the first half, coefficients of and in the long-run equilibrium

equation as well as the difference series of these variables in the short-run adjustment equation are not

significant; but in the second half, almost all of these coefficients become significant. In addition, the

coefficient of also becomes negative and significant in the second half. Furthermore, the

estimated parameter of is positive in the first half, but switches to negative in the second half. The

first-half results signify that increases in term spreads lead to an expansion of credit risk spreads. This

phenomenon has also been confirmed in Blanco et al. (2005), but there is no consensus as to the

underlying mechanism. In any case, we could say that these results suggest the possibility that,

following the onset of the financial crisis, CDS markets have become more easily susceptible to trends

in other financial markets and in the overall financial market. Third, whereas the adjustment parameter

21 June 2007 is the period when the failure by a hedge fund under the control of Bear Stearns in subprime loan

investments was viewed with apprehension in the marketplace, and when subprime-related securitized papers began to be

downgraded.


- 15 -

is -0.003 to -0.005 in the first half, it declines as far as -0.012 to -0.016 in the second half.22

The fact

that the negative range of the adjustment parameter becomes broader suggests that CDS spreads are

moving toward convergence at the long-run equilibrium level at a greater speed.23

4.4.2. Principal component analysis

In the analyses thus far, it is found that the explanatory power is limited no matter how we formulate

the model, except for the time series model using level variables as the dependent variable, for which

there is another concern of spurious regression. Previous studies on the U.S. and European credit

markets report somewhat paradoxical outcomes; the majority of variation in credit spreads that cannot

be captured through regression analysis ends up being explained using some systemic factors.24

I will

examine whether such a phenomenon can also be observed in the Japanese CDS market. Specifically, I

will use principal component analysis to investigate how much of the CDS spread’s fluctuations can be

explained by unobservable common factors.

Table 10 shows the results of the principal component analysis conducted on the four variables;

, , and two residual series from the full models with or as a

dependent variable. Principal component analysis has been separately conducted on samples before and

after the financial crisis. Looking at Table 10, we can confirm that the contribution ratio of the first

principal component of the original series ( , ) increases in the second half. This

suggests that, some factors common to the sample firms become the main determinants of credit risk

during the second half. A similar trend can also be observed for the first principal component of the

residual series of . In other words, it would seem that systemic factors that cannot be fully

understood using explanatory variables in the full model become the main variation factors in

, especially during the second half. Figure 1 is a scatter diagram, with the eigenvector of the

first principal component calculated from the original series of on the horizontal axis, and

the eigenvector of the first principal component calculated from the residuals of the full model on the

vertical axis. As the figure clearly shows, there is a strong positive correlation between them. This

suggests the possibility that systemic factors included in the original series remain in the residuals

without being fully captured even by regression analysis. In light of these results, it is expected that

some systemic factors other than the explanatory variables adopted in the estimation model are causing

fluctuation of CDS spreads.

4.4.3. Discussion

The abovementioned analyses suggest that the price formation in the CDS markets changed around

the time of the financial crisis. Results of the DHP model confirm that the significance of each

22 Even if the estimation periods are changed in various ways, for the most part, these patterns can be confirmed. 23 This does not necessarily mean that CDS spreads are being determined close to the long-run equilibrium level. In other

words, despite the adjustment speed accelerating, it is feasible that the gap between the CDS spreads and the long-run

equilibrium during the second half period will be broader than that in the first half. 24 See Collin-Dufresne et al. (2001), Ericsson et al. (2009) and Di Cesare and Guazzarotti (2010).


- 16 -

explanatory variable and the overall fitness of the model improved after the financial crisis. These

finding are arguably contrary to the previous studies on the U.S. and European markets.25

What are the

reasons for the explanatory power of the model to improve amid the crisis? The first thing that comes to

mind is the possibility that the Japanese CDS market has begun to be strongly influenced by market

trends in foreign countries, in particular in the U.S. stock market. This is confirmed by the coefficients

of . Pan and Singleton (2006), for instance, also confirm that the U.S. VIX index has a significantly

positive effect on the CDS spreads whose reference entity is the Japanese government or major Japanese

banks. In contrast, to the best of the author’s knowledge, no empirical finding has been reported on the

U.S. and European markets, which shows that adding the VIX index as an independent variable

improves the explanatory power of a model after the onset of the financial crisis. Second, CDS spreads

seem to have been determined with a fair degree of “independence” from the bond and stock markets

prior to the financial crisis. One of the notable features of the analyses before the financial crisis is that

almost all the variables that are related to the other financial market — such as , and —

are not significant while the coefficients of and are significant. This suggests

that the interconnection between CDS market and bond/stock market did not manifest before the

financial crisis. In other words, the onset of the crisis has led to various transactions extending across

these markets, and as a result, the information efficiency of market prices has improved. The changes in

the adjustment parameter seen in Table 9 indirectly support this hypothesis.

On the other hand, the results of the principal component analysis suggest that systemic factors

common to all firms triggered fluctuations of CDS spreads during the financial crisis. The question of

what these systemic factors are is an issue for the future research. However, given that it is getting clear

that liquidity is having a notable impact on price formation in the U.S. CDS markets, and that variables

related to the overall liquidity of CDS markets and to the liquidity of individual CDSs have not been

considered in this paper, liquidity might be related to the systemic factors. As of the time of writing this

paper, there are no public data on both overall liquidity of the Japanese CDS market and liquidity of

individual CDSs. When relevant data become accessible, we will need to confirm the effect of the

liquidity on price formation in the Japanese CDS market.

5. Conclusion

In this paper, I examined the pricing of the Japanese CDSs in which non-financial corporations are

the reference entity. I relied on a simple time series model and DHP model, focusing on structural

variables and other state variables that capture financial market and macroeconomic trends. The results

confirm that price formation mechanisms suggested by the structural model are at work, but that price

fluctuations in the CDS market cannot be fully explained even using structural variables and other

25 For a comparison before and after the financial crisis and the effects of VIX, see Di Cesare and Guazzarotti (2010),

Ferrucci (2003), and Greatrex (2008). For the effects of liquidity, see Driessen (2005), Tang and Yan (2008), Acharya et

al. (2008), Bongaerts et al. (2008, 2011), and Nashikkar et al. (2009).


- 17 -

market variables. I also point out that, price formation in CDS markets changed when the financial crisis

hit, and some kind of systemic factors have been influencing CDS spreads particularly since the onset of

the financial crisis.

In conclusion, I will summarize the implications derived from these results, separated into

suggestions for research and significance for public policy and financial business. With respect to the

suggestions for future research, first, it can be pointed out that using a model like the DHP model, which

allows heterogeneous parameters and long-run equilibrium relationships, is preferable when estimating

CDS spreads. While time series models and panel analyses with homogeneous parameter restrictions

have been widely used in existing studies, the results in this paper show the possible superiority of the

DHP model over the existing quantitative models. It should be noted that in addition to structural

variables, a range of variables that capture market trends need to be incorporated as determinants of

CDS spreads. In particular, given that U.S. VIX has high explanatory power in analyses in this paper,

effects from overseas need to be taken into full account when estimating the determinants of credit risk

in domestic markets. Second, the CDS market seems not to have been linked to the bond and stock

markets for the pre-crisis period. If this low-level interconnection has been caused by the lack of an

arbitrage function extending across these markets, then we should be cautious about the possibility that

the efficient allocation of resources and the risk sharing function through the CDS market have not been

fully manifested. In addition to a more detailed investigation into the interconnection between CDS

markets and other financial markets, the effects of CDS markets on economic welfare will also need to

be examined. On the other hand, the fact that CDS spread fluctuations have not been fully elucidated —

the credit spread puzzle — has important implications for financial businesses. That is, this uncertainty

in pricing will need to be fully considered when conducting CDS trading and associated risk

management. It is also expected that this puzzle will make it difficult for regulatory authorities to assess

the validity of CDS spreads. As a consequence, it may be becoming more difficult to identify unfair

trading related to CDS markets.


- 18 -

Appendix: Derivation of Firm Value Volatility and the Distance-to-Default Indicator

In this appendix, I describe the method for deriving firm value volatility ( ) and the

distance-to-default measure ( ). The concept underlying the calculation of and is

the nature of equity as a call option (Black and Scholes 1972, 1973., etc.). In other words, an equity can

be viewed as the right of claim against residual assets in case where the firm value exceeds the debt

value at some point in the future (maturity). The method of derivation below follows Gropp et al. (2002).

A detailed description of the derivation and the characteristics of the DD can be found in the paper, and

so will be omitted here.

In preparation for the explanation, I shall define a number of variables as follows:

VE: market value of equity (market capitalization)

VA: firm value

D: debt value

r: risk-free interest rate

ζA: volatility of a firm’s asset value

ζE: equity volatility

T: time until the maturity of the debt liabilities

ε: standard normal distribution

N():cumulative standard normal distribution function

dz: standard Wiener process

To begin with, if we assume the premises of the basic option pricing theory by Black and Scholes

(1972), the following relationship between firm value and stock value applies.

21 dNDedNVV rTAE

Tdd

T

TrD

V

d

A

A

AA

12

2ln

1

2

）（i

Here, the following equation holds true between firm value volatility and stock volatility:

A

E

AE dN

V

V 1

）（ii

Thus, if VE, ζE, D, r, and T are once determined, we can calculate VA and ζA from equations (i) and (ii)

using convergence calculation. In this paper, VA and ζA are calculated assuming VE is market

capitalization, ζE is the (60-day) historical volatility of the stock price series, D is the book value of the

total debt liabilities, r is the yield on government bonds, and T is 1 (year). The ζA calculated by

following this procedure is the firm value volatility ( ) set forth in this paper.


- 19 -

If we consider that firm value follows the geometric Brownian motion, we get the following formula

for firm value at time t.

ttrVV AA

AtA

2lnln

2

）（iii

Here, we regard a default to be the state that firm value is less than its debt value until the maturity of

the debt. In this setting, the default probability can be defined by equation (iv), and we can define the

distance to default measure (DD) as in equation (v).

t

trD

V

NP

A

AA

t

2ln

2

）（iv

t

trD

V

DD

A

AA

t

2

ln2

）（v

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- 22 -

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- 23 -

Table 1: Definition of Variables

Nam

e o

f v

ari

ab

leD

efi

nit

ion

So

urc

e

CD

SS

Lev

el v

alu

e o

f C

DS

sp

read

J-C

DS

data

base p

ub

lish

ed

by

To

ky

o F

inan

cia

l E

xch

an

ge I

nc.

ln(C

DS

S)

Natu

ral lo

gari

thm

of

CD

SS

〃

⊿C

DS

SC

DS

S a

t ti

me t

min

us C

DS

S a

t ti

me t

-1〃

⊿ln

(CD

SS

)ln

(CD

SS

) a

t ti

me t

min

us l

n(C

DS

S)

at

tim

e t

-1〃

LE

VE

RA

GE

{D

eb

t T

ota

l ÷

(Deb

t T

ota

l＋M

ark

et

Valu

e o

f E

qu

ity

)} is t

ran

sfo

med

to

mo

nth

ly d

ata

usin

g lin

ear

inte

rpo

lati

on

meth

od

. F

inan

cia

l d

ata

are

sem

ian

nu

al.

Co

llecte

d b

y A

str

a M

an

ag

er

data

base (

QU

ICK

)

VO

LA

TIL

ITY

Calc

ula

ted

based

on

th

e p

roced

ure

in

Ap

pen

dix

.〃

RF

Inte

rest

rate

on

10 y

ear

go

vern

men

t b

on

d in

th

e s

eco

nd

ary

mark

et

〃

TS

Inte

rest

rate

on

10 y

ear

go

vern

men

t b

on

d -

in

tere

st

rate

on

1 y

ear

go

vern

men

t b

on

d〃

TO

PIX

Dif

fere

ce o

f n

atu

ral lo

gari

thm

of

TO

PIX

In

dex

at

tim

e t

co

mp

are

d t

o p

rev

iou

s d

ay

〃

ln(M

V)

Natu

ral lo

gari

thm

of

Mark

et

Valu

e o

f E

qu

ity

〃

SW

AP

TIO

NIm

plied

vo

lati

lity

of

Sw

ap

tio

n（

5 y

ears

, 1 m

on

th m

atu

rity

)B

loo

mb

erg

VIX

Imp

lied

vo

lati

tily

of

S&

P500 in

dex

〃


- 24 -

Table 2: List of Sample

（1）Name of reference entity

Security ID Name of firm Security ID Name of firm

4005 Sumitomo Chemical Company, Limited 8031 Mitsui & Co., Ltd.

4183 Mitsui Chemicals, Inc. 8053 Sumitomo Corporation

5001 Nippon Oil Corporation 8058 Mitsubishi Corporation

5401 Nippon Steel Corporation 8515 Aiful Corporation

5802 Sumitomo Electric Industries, Ltd 8564 Takefuji Corporation

6501 Hitachi, Ltd. 8572 Acom Co., Ltd.

6502 Toshiba Corporation 8574 Promise Co., Ltd.

6503 Mitsubishi Electric Corporation 8591 ORIX Corporation

6701 NEC Corporation 8801 Mitsui Fudosan Co., Ltd.

6702 Fujitsu Limited 8802 Mitsubishi Estate Co., Ltd.

6752 Panasonic Corporation 9005 Tokyu Corporation

6753 Sharp Corporation 9041 Kintetsu Corporation

6758 Sony Corporation 9042 Hankyu Hanshin Holdings, Inc.

6764 SANYO Electric Co., Ltd. 9202 All Nippon Airways Co., Ltd.

6952 Casio Computer Co., Ltd. 9205 Japan Airlines Corporation

7011 Mitsubishi Heavy Industries, Ltd. 9433 KDDI Corporation

7012 Kawasaki Heavy Industries, Ltd. 9437 NTT DOCOMO, INC.

7201 Nissan Motor Co.,Ltd. 9501 The Tokyo Electric Power Company,

7203 Toyota Motor Corporation 9502 Chubu Electric Power Co.,Inc.

7267 Honda Motor Co., Ltd. 9503 The Kansai Electric Power Company,

7269 SuzukiI Motor Corporation 9531 Tokyo Gas Co., Ltd.

7731 Nikon Corporation 9532 Osaka Gas Co., Ltd.

7752 Ricoh Company, Ltd.

（2）By rating class

# of firms share # of firms share # of firms share

AAA 1 2.2% 1 2.2% 1 2.2%

AA+ 7 15.6% 7 15.6% 7 15.6%

AA 4 8.9% 4 8.9% 3 6.7%

AA- 6 13.3% 7 15.6% 8 17.8%

A+ 6 13.3% 8 17.8% 7 15.6%

A 8 17.8% 8 17.8% 8 17.8%

A- 5 11.1% 3 6.7% 4 8.9%

BBB+ 4 8.9% 2 4.4% 1 2.2%

BBB 3 6.7% 4 8.9% 3 6.7%

BB+ 1 2.2% 1 2.2% 1 2.2%

BB- 0 0.0% 0 0.0% 1 2.2%

CCC+ 0 0.0% 0 0.0% 1 2.2%

Total 45 100.0% 45 100.0% 45 100.0%

Rating is the R&I's long-term domestic-currency credit rating.

2004/4/1 2007/6/29 2009/9/30Rating


- 25 -

Table3: Summary Statistics

（1）

Basic

Sta

tisti

cs

Nam

e o

f v

ari

ab

leO

bs

Mean

S.D

.M

inM

ax

CD

SS

60,7

50

89.2

56

334.0

47

2.5

00

7654.9

60

ln(C

DS

S)

60,7

50

3.3

56

1.2

04

0.9

16

8.9

43

LE

VE

RA

GE

60,7

50

0.1

57

0.0

94

0.0

18

0.9

04

VO

LA

TIL

ITY

60,7

50

0.2

89

0.1

44

0.0

57

1.3

57

RF

60,7

50

0.0

15

0.0

02

0.0

12

0.0

20

SW

AP

TIO

N60,6

15

46.8

35

10.4

04

25.3

00

84.0

00

TS

60,7

50

0.0

12

0.0

02

0.0

07

0.0

19

TO

PIX

60,7

50

0.0

00

0.0

16

-0.1

00

0.1

29

ln(M

V)

60,7

50

27.9

96

0.9

42

23.3

06

31.0

36

VIX

58,7

70

20.4

74

12.0

24

9.8

90

80.8

60

（2）

Co

rrela

tio

n

CD

SS

ln(C

DS

S)

Levera

ge

ζA

rfS

wa

pti

on

TS

⊿ln

(TO

PIX

)L

n(M

V)

VIX

CD

SS

1

ln(C

DS

S)

0.5

914*

1

LE

VE

RA

GE

0.5

606*

0.6

170*

1

VO

LA

TIL

ITY

0.1

881*

0.4

829*

0.1

039*

1

RF

-0.1

661*

-0.3

275*

-0.2

311*

-0.1

136*

1

SW

AP

TIO

N0.0

193*

0.1

206*

0.1

344*

-0.0

092*

-0.3

888*

1

TS

-0.1

329*

-0.3

194*

-0.0

951*

-0.3

995*

0.2

970*

0.3

429*

1

TO

PIX

0.0

01

-0.0

138*

-0.0

184*

-0.0

182*

0.0

219*

-0.0

05

0.0

774*

1

ln(M

V)

-0.3

861*

-0.5

299*

-0.4

837*

-0.1

422*

0.1

793*

-0.1

343*

0.0

220*

0.0

107*

1

VIX

0.2

933*

0.5

918*

0.2

971*

0.6

419*

-0.3

397*

0.1

747*

-0.5

276*

-0.0

979*

-0.1

856*

1

* r

efe

rs t

o t

he s

tati

sti

cal sig

nif

ican

ce a

t th

e 5

% lev

el.


- 26 -

Table3 (continued)

（3）

Un

it R

oo

t T

est

（3）

-1. F

irm

sp

ecif

ic v

ari

ab

les

1%

5%

10%

1%

5%

10%

CD

SS

63

045

00

ln(C

DS

S)

00

043

20

VO

LA

TIL

ITY

73

045

00

LE

VE

RA

GE

00

037

30

ln(M

V)

11

038

40

1%

5%

10%

1%

5%

10%

CD

SS

10

045

00

ln(C

DS

S)

00

045

00

VO

LA

TIL

ITY

41

045

00

LE

VE

RA

GE

11

045

00

ln(M

V)

11

045

00

Th

e n

um

ber

in t

he t

ab

le is t

he n

um

ber

of

firm

s f

or

wh

ich

th

e n

ull h

yp

ote

sis

is r

eje

cte

d. T

ota

l n

um

ber

of

sam

ple

s is 4

5.

（3）

-2. v

ari

ab

les c

om

mo

n t

o f

irm

s

RF

-2.4

7-9

.48

**

*-2

.78

-38.8

3*

**

SW

AP

TIO

N-2

.23

-0.4

1-4

.31

**

*-5

0.8

9*

**

TS

-2.7

7*

-8.6

3*

**

-2.8

7-3

9.0

2*

**

TO

PIX

-36.9

2*

**

-0.5

2-3

7.9

7*

**

-358.7

9*

**

VIX

-1.7

3-2

7.8

5*

**

-2.7

7-4

4.1

7*

**

**

*, *

*, an

d *

refe

r to

th

e s

tati

sti

cal sig

nif

ican

ce a

t 1%

, 5%

, an

d 1

0%

resp

ecti

vely

.

DF

-GL

S t

est

PP

test

Lev

el

Fir

st

dif

fere

nce

Lev

el

Fir

st

dif

fere

nce

Lev

el

Fir

st

dif

fere

nce

DF

-GL

S t

est

PP

test

Lev

el

Fir

st

dif

fere

nce


- 27 -

Table4: Time Series Regression (Level Variable)

ad

j-R

2, F

-valu

e, o

bs, co

ef,

s.e

. are

cro

ss-s

ecti

on

al av

era

ge o

f esti

mati

on

resu

lts f

or

each

fir

m. F

igu

res in

pare

nth

eses a

re c

ross-s

ecti

on

la m

ed

ian

fo

r co

ef

an

d s

.e. R

ob

ust

sta

nd

ard

err

os a

re u

sed

in

OL

S. t-

valu

e a

nd

p-v

alu

e a

re t

he t

-valu

e

an

d p

-valu

e p

ert

ain

ing

to

th

e c

on

sta

nt

term

fro

m t

he O

LS

esti

mati

on

in

wh

ich

dep

en

den

t v

ari

ab

le c

on

sis

t o

f th

e p

ara

mete

r esti

mate

s d

eri

ved

fro

m O

LS

reg

ressio

ns f

or

each

fir

m w

hile e

xpla

nato

ry v

ari

ab

le is a

co

nsta

nt

term

. T

he c

oef

an

d

s.e

. fo

r S

QR

(RF

) are

exp

ressed

dev

ided

by

10000.

t-v

alu

ep

-valu

et-

valu

ep

-valu

et-

valu

ep

-valu

e

LE

VE

RA

GE

859

<524>

59

<40>

3.4

10

0.0

01

1,1

59

<795>

232

<136>

1.2

50

0.2

17

1,1

04

<794>

226

<135>

1.9

00

0.0

65

VO

LA

TIL

ITY

218

<131>

22

<6.5

6>

3.0

20

0.0

04

174

<89>

20

<6.6

4>

3.5

80

0.0

01

62

<48>

23

<11>

2.5

70

0.0

14

RF

-8,9

82

<-2

,479>

955

<364>

-2.7

30

0.0

09

-100,9

80

<-3

3,2

44>

11,4

75

<5,1

46>

-3.9

60

0.0

00

-92,3

53

<-3

8,5

52>

10,8

31

<5,1

13>

-4.1

60

0.0

00

SQ

R(R

F)

－－

279

<100>

36

<16>

4.0

10

0.0

00

249

<107>

33

<16>

4.3

00

0.0

00

TS

－－

13,2

35

<935>

1,2

42

<489>

1.6

90

0.0

98

16,0

06

<2,4

22>

1,2

32

<522>

2.1

80

0.0

35

TO

PIX

－－

206

<116>

112

<56>

5.7

90

0.0

00

254

<133>

119

<58>

5.6

90

0.0

00

Ln

(MV

)－

－3.9

0<

-7.2

0>

35

<14>

0.0

30

0.9

80

27

<25>

33

<16>

0.2

90

0.7

72

SW

AP

TIO

N－

－-0

.502

<-0

.053>

0.2

07

<0.0

92>

-0.8

60

0.3

96

-1.0

09

<-0

.278>

0.2

14

<0.0

96>

-2.1

00

0.0

41

VIX

－－

－－

1.6

83

<0.4

91>

0.3

67

<0.1

81>

2.1

80

0.0

34

co

nst

an

t24.2

7<

-23.1

9>

20.0

0<

7.8

2>

0.3

60

0.7

19

411

<107>

996

<371>

0.0

90

0.9

27

-306

<-3

31>

930

<483>

-0.1

20

0.9

08

ad

j-R

2

F-v

alu

e

ob

s

t-v

alu

ep

-valu

et-

valu

ep

-valu

et-

valu

ep

-valu

e

LE

VE

RA

GE

14

<9.1

88>

0.5

64

<0.4

41>

4.5

70

0.0

00

6.2

93

<1.2

04>

1.8

74

<1.5

63>

0.9

70

0.3

38

5.0

20

<5.6

08>

1.9

27

<1.5

72>

0.8

50

0.4

01

VO

LA

TIL

ITY

3.4

32

<3.3

64>

0.1

29

<0.1

19>

13.9

70

0.0

00

2.5

07

<2.2

51>

0.1

30

<0.1

24>

13.7

90

0.0

00

1.8

62

<1.7

57>

0.1

67

<0.1

52>

12.2

10

0.0

00

RIS

KF

RE

E-6

2<

-57>

6.6

71

<6.3

83>

-7.5

90

0.0

00

-613

<-5

84>

83.0

13

<77>

-11.0

00

0.0

00

-603

<-6

31>

80

<77>

-12.4

20

0.0

00

SQ

R(R

F)

－－

1.8

87

<1.7

40>

0.2

57

<0.2

42>

11.6

90

0.0

00

1.8

40

<1.8

36>

0.2

49

<0.2

39>

13.2

60

0.0

00

TS

－－

-33

<-2

7>

7.8

42

<7.1

76>

-2.4

00

0.0

21

-16

<-5

.017>

8.3

92

<8.0

06>

-1.2

80

0.2

07

TO

PIX

－－

1.3

30

<1.3

10>

0.7

08

<0.6

89>

11.5

50

0.0

00

1.6

11

<1.6

20>

0.7

58

<0.7

50>

13.1

10

0.0

00

ln(M

V)

－－

-0.9

61

<-1

.499>

0.2

20

<0.1

83>

-1.3

20

0.1

93

-0.9

50

<-1

.047>

0.2

19

<0.1

86>

-1.5

60

0.1

26

SW

AP

TIO

N－

－0.0

06

<0.0

05>

0.0

01

<0.0

01>

4.5

00

0.0

00

0.0

04

<0.0

04>

0.0

02

<0.0

01>

3.5

70

0.0

01

VIX

－－

－－

0.0

09

<0.0

07>

0.0

02

<0.0

02>

3.4

80

0.0

01

co

nst

an

t1.8

68

<1.4

24>

0.1

47

<0.1

35>

6.1

60

0.0

00

34

<51>

6.3

21

<5.2

02>

1.6

30

0.1

11

34

<32>

6.3

14

<5.3

42>

1.9

10

0.0

63

ad

j-R

2

F-v

alu

e

ob

s1,3

50

1,3

47

1,3

03

－

0.7

40.8

30.8

5

1,7

99

1,0

74

1,0

39

－

－－

－－

－－

－－

－－

－－

1,3

50

1,3

47

1,3

03

y=

ln(C

DS

S)

co

ef

s.e

.co

ef

s.e

.co

ef

s.e

.

545

356

343

－－

－－

－－

－－

0.6

70.7

70.7

9

－－

－－

－－

y=

CD

SS

co

ef

s.e

.co

ef

s.e

.co

ef

s.e

.


- 28 -

Table 5: Time Series Regression (Differenced Variable)

ad

j-R

2, F

-valu

e, o

bs, co

ef,

s.e

. are

cro

ss-s

ecti

on

al av

era

ge o

f esti

mati

on

resu

lts f

or

each

fir

m. F

igu

res in

pare

nth

eses a

re c

ross-s

ecti

on

la m

ed

ian

fo

r co

ef

an

d s

.e. R

ob

ust

sta

nd

ard

err

os a

re u

sed

in

OL

S. t-

valu

e a

nd

p-v

alu

e a

re t

he t

-valu

e

an

d p

-valu

e p

ert

ain

ing

to

th

e c

on

sta

nt

term

fro

m t

he O

LS

esti

mati

on

in

wh

ich

dep

en

den

t v

ari

ab

le c

on

sis

t o

f th

e p

ara

mete

r esti

mate

s d

eri

ved

fro

m O

LS

reg

ressio

ns f

or

each

fir

m w

hile e

xpla

nato

ry v

ari

ab

le is a

co

nsta

nt

term

. T

he c

oef

an

d

s.e

. fo

r S

QR

(RF

) are

exp

ressed

as d

ivid

ed

by

10000.

t-v

alu

ep

-valu

et-

valu

ep

-valu

et-

valu

ep

-valu

e

⊿L

EV

ER

AG

E213

<127>

76

<39>

4.9

00

0.0

00

130

<38>

90

<53>

2.7

20

0.0

09

131

<25>

94

<46>

2.6

40

0.0

11

⊿V

OL

AT

ILIT

Y28

<11>

27

<13>

2.7

50

0.0

09

24

<8.4

80>

27

<13>

2.4

20

0.0

20

26

<7.9

94>

30

<13>

2.4

70

0.0

17

⊿R

F-3

30

<-2

35>

447

<187>

-2.4

50

0.0

18

-8.3

33

<25>

469

<199>

-0.0

70

0.9

44

-80

<-5

.953>

470

<186>

-0.7

90

0.4

35

⊿S

QR

(RF

)－

－-9

.627

<-2

.826>

73

<32>

-0.4

30

0.6

66

-25

<-7

.387>

75

<31>

-0.9

70

0.3

37

TS

－－

-45

<-5

0>

100

<28>

-1.0

10

0.3

17

-29

<-3

9>

104

<28>

-0.5

80

0.5

67

TO

PIX

－－

-21

<-2

1>

21

<9.1

12>

-2.4

40

0.0

19

-5.9

15

<-1

3>

23

<9.6

36>

-0.5

40

0.5

92

ln(M

V)

－－

-1.3

22

<-0

.287>

1.0

32

<0.2

81>

-2.6

70

0.0

11

-1.2

94

<-0

.187>

1.0

58

<0.2

65>

-2.4

30

0.0

19

⊿S

WA

PT

ION

－－

0.0

13

<0.0

03>

0.0

62

<0.0

22>

0.8

50

0.4

00

0.0

05

<0.0

01>

0.0

67

<0.0

23>

0.2

60

0.7

97

⊿V

IX－

－－

－0.2

12

<0.0

74>

0.1

33

<0.0

56>

3.6

50

0.0

01

co

nst

an

t0.2

58

<0.0

21>

0.1

56

<0.0

68>

1.9

90

0.0

53

37

<8.4

55>

28

<8.3

60>

2.7

40

0.0

09

36

<5.9

62>

29

<7.9

05>

2.4

80

0.0

17

ad

j-R

2

F-v

alu

e

ob

s

t-v

alu

ep

-valu

et-

valu

ep

-valu

et-

valu

ep

-valu

e

⊿L

EV

ER

AG

E1.8

76

<1.6

56>

0.4

51

<0.3

61>

8.2

20

0.0

00

0.7

16

<0.4

26>

0.5

20

<0.4

24>

3.5

00

0.0

01

0.6

72

<0.3

54>

0.5

18

<0.4

16>

3.7

40

0.0

01

⊿V

OL

AT

ILIT

Y0.3

23

<0.3

05>

0.1

61

<0.1

56>

11.6

50

0.0

00

0.2

71

<0.2

60>

0.1

55

<0.1

49>

10.0

00

0.0

00

0.2

42

<0.2

29>

0.1

52

<0.1

44>

9.1

70

0.0

00

⊿R

F-6

.755

<-7

.354>

3.0

55

<2.8

96>

-12.7

20

0.0

00

-2.0

64

<-1

.608>

3.0

18

<2.9

31>

-5.4

70

0.0

00

-2.7

03

<-2

.523>

3.0

52

<2.9

94>

-7.3

70

0.0

00

⊿S

QR

(RF

)－

－0.3

27

<0.3

74>

0.6

93

<0.6

56>

4.1

20

0.0

00

0.2

04

<0.2

09>

0.7

03

<0.6

72>

2.5

50

0.0

14

TS

－－

-0.8

73

<-0

.870>

0.3

88

<0.3

44>

-15.4

10

0.0

00

-0.7

64

<-0

.739>

0.3

76

<0.3

41>

-14

0.0

00

TO

PIX

－－

-0.3

08

<-0

.319>

0.0

92

<0.0

92>

-16.3

90

0.0

00

-0.1

73

<-0

.185>

0.0

96

<0.0

93>

-9.4

20

0.0

00

ln(M

V)

－－

-0.0

02

<-0

.002>

0.0

03

<0.0

03>

-2.6

20

0.0

12

-0.0

02

<-0

.002>

0.0

03

<0.0

03>

-2.5

70

0.0

14

⊿S

WA

PT

ION

－－

0.0

003

<0.0

00>

0.0

00

<0.0

00>

8.5

60

0.0

00

0.0

002

<0.0

00>

0.0

00

<0.0

00>

5.7

10

0.0

00

⊿V

IX－

－－

－0.0

01

<0.0

01>

0.0

01

<0.0

01>

24

0.0

00

co

nst

an

t0.0

01

<0.0

01>

0.0

01

<0.0

01>

9.2

90

0.0

00

0.0

71

<0.0

62>

0.0

93

<0.0

83>

3.0

80

0.0

04

0.0

70

<0.0

55>

0.0

95

<0.0

85>

2.9

40

0.0

05

ad

j-R

2

F-v

alu

e

ob

s1,3

50

1,3

45

1,2

57

－－

0.0

40.0

60.0

7

10.3

36.3

96.3

4

－－

－－

－－

－－

－－

－－

1,3

50

1,3

45

1,2

57

y=⊿

ln(C

DS

S)

co

ef

s.e

.co

ef

s.e

.co

ef

s.e

.

7.4

95.8

05.0

0

－－

－－

－－

－－

0.0

30.0

60.0

6

－－

－－

－－

y=⊿

CD

SS

co

ef

s.e

.co

ef

s.e

.co

ef

s.e

.


- 29 -

Table6: PMG Model (without Restriction, Full Sample)

χ2 is t

he t

est

sta

tisti

cs f

or

the n

ull h

yp

oth

esis

th

at

para

mete

rs a

re h

om

og

en

eo

us, an

d f

igu

res in

pare

nth

eses a

re a

sso

cia

ted

p-v

alu

e. T

he c

oef

an

d s

.e. fo

r S

QR

(RF

) an

d ⊿

SQ

R(R

F)

are

exp

ressed

as d

ivid

ed

by

10000. F

igu

res in

lon

g-r

un

eq

uilib

riu

m e

qu

ati

on

are

resu

lts a

bo

ut

ho

mo

gen

eo

us p

ara

mete

rs. c

oef

of

oth

er

exp

lan

ato

ry v

ari

ab

les a

re c

ross-s

ecti

on

al av

era

ge o

f co

eff

icie

nts

fo

r each

fir

ms. s

.e., z

-valu

e, an

d p

-valu

e o

f th

ese v

ari

ab

les a

re t

he

sta

nd

ard

err

or,

z-v

alu

es a

nd

p-v

alu

es r

ela

tin

g t

o t

he c

on

sta

nt

term

in

th

e O

LS

esti

mati

on

in

wh

ich

th

e p

ara

mete

r esti

mate

s o

f each

issu

e a

re t

he d

ep

en

den

t v

ari

ab

le w

hile t

he c

on

sta

nt

term

is e

xpla

nato

ry v

ari

ab

le. ad

j-R

2 is

cro

ss-s

ecti

on

al av

era

ge. T

he r

esu

lts o

n c

on

sta

nt

term

s a

re o

mit

ted

.

Pan

el A

: d

ep

en

den

t v

ari

ab

le＝

⊿C

DS

S

co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)(i

)co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)(i

)co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)(i

)

lon

g-t

erm

eq

uati

on

LE

VE

RA

GE

491

33

14.7

50

0.0

00

920

105

8.7

20

0.0

00

629

57

11.0

40

0.0

00

VO

LA

TIL

ITY

289

10

27.9

50

0.0

00

205

16

12.9

70

0.0

00

177

8.7

45

20.2

00

0.0

00

RF

-2,7

03

616

-4.3

90

0.0

00

-196,0

53

15,7

09

-12.4

80

0.0

00

-106,4

00

8,1

33

-13.0

80

0.0

00

SQ

R(R

F)

(ii)

－－

－－

657

51

12.9

20

0.0

00

355

26

13.6

60

0.0

00

TS

－－

－－

-20,2

36

1,3

84

-14.6

20

0.0

00

-10,1

69

656

-15.5

00

0.0

00

TO

PIX

－－

－－

-7,8

58

455

-17.2

70

0.0

00

-3,7

19

180

-20.6

30

0.0

00

ln(M

V)

－－

－－

69

15

4.7

00

0.0

00

41

7.6

10

5.4

40

0.0

00

SW

AP

TIO

N－

－－

－5.3

94

0.3

67

14.7

00

0.0

00

2.9

99

0.1

72

17.4

10

0.0

00

sh

ort

-term

eq

uati

on

ad

just

men

t p

ara

mer

ter

(ϕi)

-0.0

06

0.0

01

-7.4

50

0.0

00

487.5

5(0

.0000)

-0.0

05

0.0

01

-8.1

30

0.0

00

474.9

1(0

.0000)

-0.0

07

0.0

01

-8.5

70

0.0

00

805.8

0(0

.0000)

⊿L

EV

ER

AG

E205

43

4.7

20

0.0

00

646.9

5(0

.0000)

252

91

2.7

80

0.0

05

282.2

8(0

.0000)

238

97

2.4

40

0.0

15

279.8

5(0

.0000)

⊿V

OL

AT

ILIT

Y24

10

2.3

90

0.0

17

157.0

5(0

.0000)

20

11

1.8

30

0.0

67

164.9

9(0

.0000)

22.3

91

12

1.8

70

0.0

62

174.0

4(0

.0000)

⊿R

F-3

25

136

-2.3

90

0.0

17

43.2

8(0

.5023)

511

275

1.8

60

0.0

63

11.2

4(1

.0000)

525

297

1.7

70

0.0

77

12.9

6(1

.0000)

⊿S

QR

(RF

)(i

i)－

－－

－－

-42

18

-2.3

50

0.0

19

20.2

6(0

.9992)

-59

18.6

97

-3.1

40

0.0

02

21.7

5(0

.9980)

⊿T

S－

－－

－－

-1,0

34

382

-2.7

10

0.0

07

13.0

6(1

.0000)

-1,0

32

359

-2.8

80

0.0

04

12.2

8(1

.0000)

⊿T

OP

IX－

－－

－－

23

3.1

10

7.2

80

0.0

00

388.3

5(0

.0000)

23

3.9

61

5.8

20

0.0

00

377.6

0(0

.0000)

⊿ln

(MV

)－

－－

－－

15

20.7

72

0.7

30

0.4

65

190.1

4(0

.0000)

12

23.1

17

0.5

30

0.5

95

186.4

8(0

.0000)

⊿S

WA

PT

ION

－－

－－

－0.0

11

0.0

17

0.6

70

0.5

02

41.0

5(0

.5987)

0.0

03

0.0

16

0.1

80

0.8

56

43.2

7(0

.5029)

⊿V

IX－

－－

－－

－－

－－

－0.1

94

0.0

56

3.4

50

0.0

01

187.0

3(0

.0000)

log

lik

elih

oo

d

ad

j-R

2

ob

s60,7

49

60,5

24

56,5

64

-146,9

88

-144,9

97

-132,1

44

0.0

40.0

80.2

3

PM

GP

MG

PM

G


- 30 -

Table6 (continued)

Pan

el B

: d

ep

en

den

t v

ari

ab

le＝

⊿ln

(CD

SS

)

co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)1

co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)1

co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)1

lon

g-t

erm

eq

uati

on

LE

VE

RA

GE

8.6

04

0.6

58

13.0

80

0.0

00

6.7

16

1.0

23

6.5

70

0.0

00

7.7

84

1.0

13

7.6

80

0.0

00

VO

LA

TIL

ITY

5.9

88

0.2

45

24.4

20

0.0

00

2.7

50

0.1

86

14.8

20

0.0

00

2.9

70

0.1

84

16.1

30

0.0

00

RF

-88

14

-6.1

20

0.0

00

-2,8

97

182

-15.9

00

0.0

00

-2,5

69

175

-14.6

70

0.0

00

SQ

R(R

F)

(ii)

－－

－－

10

0.5

87

16.2

10

0.0

00

8.5

44

0.5

64

15.1

40

0.0

00

TS

－－

－－

-314

16

-19.9

30

0.0

00

-281

15

-18.9

50

0.0

00

TO

PIX

－－

－－

-97

4.7

10

-20.5

50

0.0

00

-73.1

3.9

08

-18.7

10

0.0

00

ln(M

V)

－－

－－

-0.0

37

0.1

61

-0.2

30

0.8

19

0.0

26

0.1

59

0.1

60

0.8

71

SW

AP

TIO

N－

－－

－0.0

54

0.0

03

16.2

90

0.0

00

0.0

54

0.0

03

16.4

00

0.0

00

sh

ort

-term

eq

uati

on

ad

just

men

t p

ara

mer

ter

(ϕi)

-0.0

04

0.0

00

-12.8

10

0.0

00

138.9

2(0

.0000)

-0.0

06

0.0

00

-29.4

00

0.0

00

125.7

4(0

.0000)

-0.0

06

0.0

00

-24.3

50

0.0

00

125.9

9(0

.0000)

⊿L

EV

ER

AG

E1.8

32

0.2

27

8.0

70

0.0

00

368.1

4(0

.0000)

0.8

75

0.3

28

2.6

70

0.0

08

138.2

9(0

.0000)

1.1

87

0.3

60

3.3

00

0.0

01

140.0

9(0

.0000)

⊿V

OL

AT

ILIT

Y0.2

93

0.0

27

10.7

70

0.0

00

212.9

0(0

.0000)

0.1

85

0.0

24

7.7

50

0.0

00

141.7

8(0

.0000)

0.1

57

0.0

23

6.7

70

0.0

00

117.6

5(0

.0000)

⊿R

F-6

.555

0.5

27

-12.4

40

0.0

00

49.3

8(0

.2668)

-7.2

14

0.9

02

-8.0

00

0.0

00

27.7

4(0

.9736)

-7.8

80

1.0

04

-7.8

50

0.0

00

35.3

0(0

.8225)

⊿S

QR

(RF

)(i

i)－

－－

－－

0.0

49

0.0

76

0.6

50

0.5

17

26.4

9(0

.9830)

-0.1

08

0.0

75

-1.4

50

0.1

46

26.3

7(0

.9838)

⊿T

S－

－－

－－

4.3

53

0.7

75

5.6

20

0.0

00

21.3

5(0

.9984)

4.4

53

0.8

66

5.1

40

0.0

00

26.2

0(0

.9848)

⊿T

OP

IX－

－－

－－

0.2

56

0.0

09

27.1

70

0.0

00

93.2

7(0

.0000)

0.2

34

0.0

09

25.5

60

0.0

00

92.2

4(0

.0000)

⊿ln

(MV

)－

－－

－－

0.0

40

0.0

37

1.0

60

0.2

87

126.1

7(0

.0000)

0.0

74

0.0

37

2.0

10

0.0

45

112.5

4(0

.0000)

⊿S

WA

PT

ION

－－

－－

－0.0

001

0.0

00

2.4

20

0.0

15

18.1

8(0

.9998)

0.0

0004

0.0

00

0.9

50

0.3

43

22.2

0(0

.9975)

⊿V

IX－

－－

－－

－－

－－

－0.0

01

0.0

00

17.1

00

0.0

00

48.3

8(0

.3007)

log

lik

elih

oo

d

ad

j-R

2

ob

s60,7

49

60,5

24

56,5

64

128,4

65

129,7

10

123,4

37

0.0

0-0

.01

0.1

3

PM

GP

MG

PM

G


- 31 -

Table7: PMG Model (With Restriction, Full Sample)

χ2 is t

he t

est

sta

tisti

cs f

or

the n

ull h

yp

oth

esis

th

at

para

mete

rs a

re h

om

og

en

eo

us, an

d f

igu

res in

pare

nth

eses a

re a

sso

cia

ted

p-v

alu

e. T

he c

oef

an

d s

.e. fo

r S

QR

(RF

) an

d ⊿

SQ

R(R

F)

are

exp

ressed

as d

ivid

ed

by

10000. F

igu

res in

lo

ng

-ru

n e

qu

ilib

riu

m e

qu

ati

on

are

resu

lts a

bo

ut

ho

mo

gen

eo

us p

ara

mete

rs. c

oef

of

oth

er

exp

lan

ato

ry v

ari

ab

les a

re c

ross-s

ecti

on

al

av

era

ge o

f co

eff

icie

nts

fo

r each

fir

ms. s

.e., z

-valu

e, an

d p

-valu

e o

f th

ese v

ari

ab

les a

re t

he s

tan

dard

err

or,

z-v

alu

es a

nd

p-v

alu

es r

ela

tin

g t

o t

he c

on

sta

nt

term

in

th

e O

LS

esti

mati

on

in w

hic

h t

he p

ara

mete

r esti

mate

s o

f each

issu

e a

re t

he d

ep

en

den

t v

ari

ab

le w

hile t

he c

on

sta

nt

term

is e

xpla

nato

ry v

ari

ab

le. ad

j-R

2 is c

ross-s

ecti

on

al av

era

ge. T

he r

esu

lts o

n c

on

sta

nt

term

s a

re o

mit

ted

.

Pan

el A

: d

ep

en

den

t v

ari

ab

le＝

⊿C

DS

S

co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)(i

)co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)(i

)

lon

g-t

erm

eq

uati

on

LE

VE

RA

GE

752

85

8.8

90

0.0

00

578

49

11.7

60

0.0

00

VO

LA

TIL

ITY

182

13

14.4

00

0.0

00

162

7.5

53

21.4

20

0.0

00

RF

-172,0

41

12,4

14

-13.8

60

0.0

00

-101,1

62

7,0

67

-14.3

20

0.0

00

SQ

R(R

F)

(ii)

575

40

14.3

30

0.0

00

336

23

14.9

00

0.0

00

TS

-18,1

66

1,1

05

-16.4

40

0.0

00

-9,9

81

577

-17.2

90

0.0

00

TO

PIX

-3,5

78

205

-17.4

30

0.0

00

-1,4

79

94

-15.6

80

0.0

00

ln(M

V)

47

12

4.0

40

0.0

00

30

6.4

02

4.7

50

0.0

00

SW

AP

TIO

N4.4

17

0.2

78

15.9

00

0.0

00

2.6

07

0.1

46

17.8

20

0.0

00

sh

ort

-term

eq

uati

on

ad

just

men

t p

ara

mer

ter

(ϕi)

-0.0

05

0.0

01

-8.5

10

0.0

00

542.6

9(0

.000)

-0.0

08

0.0

01

-8.6

60

0.0

00

830.3

7(0

.000)

⊿L

EV

ER

AG

E132.4

28

47.3

00

2.8

00

0.0

05

485.5

3(0

.000)

126.5

37

46.2

20

2.7

40

0.0

06

426.6

6(0

.000)

⊿V

OL

AT

ILIT

Y19.7

90

10.3

42

1.9

10

0.0

56

165.8

1(0

.000)

22.2

28

11.2

54

1.9

80

0.0

48

171.7

(0.0

00)

⊿R

F-1

06.8

02

140.2

11

-0.7

60

0.4

46

33.3

9(0

.8779)

-47.2

87

117.9

62

-0.4

00

0.6

89

22.7

5(0

.9967)

⊿S

QR

(RF

)(i

i)-3

2.9

19

17.5

64

-1.8

70

0.0

61

19.3

2(

0.9

996)

-46.7

29

16.5

02

-2.8

30

0.0

05

19.9

4(0

.9993)

⊿S

WA

PT

ION

0.0

08

0.0

10

0.7

90

0.4

30

35.5

0(0

.8157)

-0.0

03

0.0

10

-0.3

30

0.7

41

36.9

3(0

.7660)

⊿V

IX－

－－

－－

0.1

90

0.0

46

4.1

50

0.0

00

194.2

(0.0

00)

log

lik

elih

oo

d

ad

j-R

2

ob

s

0.0

70.2

1

60,5

24

56,5

64

PM

GP

MG

-145,6

27

-132,7

48


- 32 -

Table7 (continued)

Pan

el B

: d

ep

en

den

t v

ari

ab

le＝

⊿ln

(CD

SS

)

co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)(i

)co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)(i

)

lon

g-t

erm

eq

uati

on

LE

VE

RA

GE

6.5

81

0.9

73

6.7

60

0.0

00

7.7

31

0.9

87.9

10

0.0

00

VO

LA

TIL

ITY

2.7

48

0.1

74

16

0.0

00

2.9

48

0.1

716.8

70

0.0

00

RF

-2,8

21

167

-17

0.0

00

-2,6

14

165

-15.8

50

0.0

00

SQ

R(R

F)

(ii)

9.2

69

0.5

37

17

0.0

00

8.6

80.5

316.3

20

0.0

00

TS

-322

15

-22

0.0

00

-297.9

14.3

3-2

0.7

80

0.0

00

TO

PIX

-49

2.5

33

-19

0.0

00

-28.5

2.0

8-1

3.6

60

0.0

00

ln(M

V)

-0.1

60

0.1

51

-1.0

60

0.2

87

-0.0

82

0.1

5-0

.540

0.5

90

SW

AP

TIO

N0.0

52

0.0

03

17

0.0

00

0.0

53

0.0

017.1

40

0.0

00

sh

ort

-term

eq

uati

on

ad

just

men

t p

ara

mer

ter

(ϕi)

-0.0

06

0.0

00

-26.1

50

0.0

00

117.8

7(0

.0000)

-0.0

06

0.0

0-2

3.2

90

0.0

00

110.2

2(0

.0000)

⊿L

EV

ER

AG

E0.6

57

0.1

75

3.7

50

0.0

00

324.5

9(0

.0000)

0.5

94

0.1

54.0

70

0.0

00

284.5

1(0

.0000)

⊿V

OL

AT

ILIT

Y0.2

13

0.0

25

8.5

70

0.0

00

157.6

4(0

.0000)

0.1

78

0.0

27.4

00

0.0

00

129.3

9(0

.0000)

⊿R

F-2

.488

0.4

47

-5.5

70

0.0

00

34.6

2(0

.8436)

-2.9

94

0.4

4-6

.880

0.0

00

34.0

4(0

.8602)

⊿S

QR

(RF

)(i

i)0.1

19

0.0

78

1.5

30

0.1

25

27.1

1(0

.9787)

-0.0

50.0

8-0

.670

0.5

02

27.1

3(0

.9786)

⊿S

WA

PT

ION

0.0

00

0.0

00

4.3

50

0.0

00

20.7

4(0

.9989)

0.0

00

0.0

02.2

30

0.0

26

23.4

4(0

.9953)

⊿V

IX－

－－

－－

0.0

01

0.0

021.3

90

0.0

00

50.0

4(0

.2461)

log

lik

elih

oo

d

ad

j-R

2

ob

s

-0.0

10.1

3

60,5

24

56,5

64

PM

GP

MG

129,0

10

122,8

39


- 33 -

Table 8: PMG Model (DD, Full Sample)

χ2 is t

he t

est

sta

tisti

cs f

or

the n

ull h

yp

oth

esis

th

at

para

mete

rs a

re h

om

og

en

eo

us, an

d f

igu

res in

pare

nth

eses a

re a

sso

cia

ted

p-v

alu

e. T

he c

oef

an

d s

.e. fo

r S

QR

(RF

) an

d ⊿

SQ

R(R

F)

are

exp

ressed

as d

ivid

ed

by

10000. F

igu

res in

lo

ng

-ru

n e

qu

ilib

riu

m e

qu

ati

on

are

resu

lts a

bo

ut

ho

mo

gen

eo

us p

ara

mete

rs. c

oef

of

oth

er

exp

lan

ato

ry v

ari

ab

les a

re c

ross-s

ecti

on

al

av

era

ge o

f co

eff

icie

nts

fo

r each

fir

ms. s

.e., z

-valu

e, an

d p

-valu

e o

f th

ese v

ari

ab

les a

re t

he s

tan

dard

err

or,

z-v

alu

es a

nd

p-v

alu

es r

ela

tin

g t

o t

he c

on

sta

nt

term

in

th

e O

LS

esti

mati

on

in w

hic

h t

he p

ara

mete

r esti

mate

s o

f each

issu

e a

re t

he d

ep

en

den

t v

ari

ab

le w

hile t

he c

on

sta

nt

term

is e

xpla

nato

ry v

ari

ab

le. ad

j-R

2 is c

ross-s

ecti

on

al av

era

ge. T

he r

esu

lts o

n c

on

sta

nt

term

s a

re o

mit

ted

.

Pan

el A

: d

ep

en

den

t v

ari

ab

le＝

⊿C

DS

S

co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)(i

)co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)(i

)

lon

g-t

erm

eq

uati

on

DD

9.3

74

2.4

17

3.8

80

0.0

00

-0.2

20

0.5

82

-0.3

80

0.7

06

SQ

R(R

F)

(ii)

261

30

8.5

60

0.0

00

63

5.3

69

11.7

50

0.0

00

TS

-105,0

78

10,6

93

-9.8

30

0.0

00

-26,7

49

1,5

36

-17.4

10

0.0

00

TO

PIX

-18,7

02

1,9

51

-9.5

90

0.0

00

-3,5

49

224

-15.8

50

0.0

00

ln(M

V)

-224

29

-7.7

90

0.0

00

-75

7.0

94

-10.5

50

0.0

00

SW

AP

TIO

N22

2.3

86

9.0

80

0.0

00

5.5

01

0.3

66

15.0

20

0.0

00

sh

ort

-term

eq

uati

on

ad

just

men

t p

ara

mer

ter（

ϕi）

-0.0

02

0.0

00

-5.0

20.0

0156.6

1(0

.0000)

-0.0

04

0.0

01

-7.8

00.0

0460.0

2(0

.0000)

⊿D

D-0

.352

0.2

14

-1.6

40.1

020.7

8(0

.9989)

-0.6

50

0.4

45

-1.4

60.1

426.8

8(0

.9804)

⊿S

QR

(RF

)(i

i)-5

9.2

29

22.3

78

-2.6

50.0

122.0

7(0

.9977)

-59.3

86

20.8

79

-2.8

40.0

022.9

4(0

.9963)

⊿S

WA

PT

ION

0.0

26

0.0

27

0.9

70.3

338.8

8(0

.6903)

0.0

15

0.0

18

0.8

40.4

045.0

7(0

.4271)

⊿V

IX－

－－

－－

0.2

57

0.0

66

3.8

90.0

0217.1

9(0

.0000)

log

lik

elih

oo

d

ad

j-R

2

ob

s

0.0

50.2

0

60,5

24

56,5

64

PM

GP

MG

-146,1

43

-133,3

25


- 34 -

Table 8 (continued)

Pan

el B

: d

ep

en

den

t v

ari

ab

le＝

⊿ln

(CD

SS

)

co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)(i

)co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)(i

)

lon

g-t

erm

eq

uati

on

DD

-0.0

52

0.0

09

-5.7

40.0

0-0

.045

0.0

10

-4.4

30.0

0

SQ

R(R

F)

(ii)

0.7

20

0.0

77

9.3

50.0

00.8

98

0.0

87

10.3

00.0

0

TS

-471

25

-18.5

10.0

0-4

74

27

-17.7

20.0

0

TO

PIX

-79

4.5

47

-17.4

80.0

0-5

43.6

19

-14.9

80.0

0

ln(M

V)

-1.4

87

0.0

96

-15.5

30.0

0-1

.659

0.1

01

-16.4

50.0

0

SW

AP

TIO

N0.0

68

0.0

05

14.3

60.0

00.0

73

0.0

05

14.1

20.0

0

sh

ort

-term

eq

uati

on

ad

just

men

t p

ara

mer

ter（

ϕi）

-0.0

05

0.0

00

-37.8

80.0

0103.0

1(0

.0000)

-0.0

04

0.0

00

-31.3

30.0

080.0

8(0

.0007)

⊿D

D-0

.008

0.0

01

-6.9

60.0

0121.9

9(0

.0000)

-0.0

07

0.0

01

-6.1

00.0

0108.2

9(0

.0000)

⊿S

QR

(RF

)(i

i)-0

.008

0.0

82

-0.1

00.9

228.7

5(0

.9633)

-0.1

62

0.0

83

-1.9

40.0

529.7

2(

0.9

510)

⊿S

WA

PT

ION

0.0

00

0.0

00

5.2

60.0

020.7

1(0

.9989)

0.0

00

0.0

00

2.7

10.0

124.7

6(

0.9

915)

⊿V

IX－

－－

－－

0.0

01

0.0

00

19.9

40.0

057.3

7(0

.0851)

log

lik

elih

oo

d

ad

j-R

2

ob

s

-0.0

10.1

4

60,5

24

56,5

64

PM

GP

MG

128,5

80

122,4

42


- 35 -

Table 9: PMG Model (Before and After Crisis)

χ2 is t

he t

est

sta

tisti

cs f

or

the n

ull h

yp

oth

esis

th

at

para

mete

rs a

re h

om

og

en

eo

us, an

d f

igu

res in

pare

nth

eses a

re a

sso

cia

ted

p-v

alu

e. T

he c

oef

an

d s

.e. fo

r S

QR

(RF

) an

d ⊿

SQ

R(R

F)

are

exp

ressed

as d

ivid

ed

by

10000. F

igu

res in

lo

ng

-ru

n e

qu

ilib

riu

m e

qu

ati

on

are

resu

lts a

bo

ut

ho

mo

gen

eo

us p

ara

mete

rs. c

oef

of

oth

er

exp

lan

ato

ry v

ari

ab

les a

re c

ross-s

ecti

on

al

av

era

ge o

f co

eff

icie

nts

fo

r each

fir

ms. s

.e., z

-valu

e, an

d p

-valu

e o

f th

ese v

ari

ab

les a

re t

he s

tan

dard

err

or,

z-v

alu

es a

nd

p-v

alu

es r

ela

tin

g t

o t

he c

on

sta

nt

term

in

th

e O

LS

esti

mati

on

in w

hic

h t

he p

ara

mete

r esti

mate

s o

f each

issu

e a

re t

he d

ep

en

den

t v

ari

ab

le w

hile t

he c

on

sta

nt

term

is e

xpla

nato

ry v

ari

ab

le. ad

j-R

2 is c

ross-s

ecti

on

al av

era

ge. T

he r

esu

lts o

n c

on

sta

nt

term

s a

re o

mit

ted

.

Pan

el A

: d

ep

en

den

t v

ari

ab

le＝

⊿C

DS

S

co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)(i

)co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)(i

)

lon

g-t

erm

eq

uati

on

LE

VE

RA

GE

124

28

4.4

50

0.0

00

808

99

8.1

70

0.0

00

VO

LA

TIL

ITY

38

7.1

63

5.3

10

0.0

00

77

13

5.9

00

0.0

00

RF

-4,6

09

2,8

77

-1.6

00

0.1

09

-178,3

31

14,2

28

-12.5

30

0.0

00

SQ

R(R

F)

(ii)

4.4

24

9.3

49

0.4

70

0.6

36

593

46

12.8

80

0.0

00

TS

4,2

38

613

6.9

20

0.0

00

-19,8

25

1,5

44

-12.8

40

0.0

00

TO

PIX

44

46

0.9

50

0.3

41

-1,4

86

128

-11.6

10

0.0

00

ln(M

V)

-6.5

13

3.6

29

-1.7

90

0.0

73

-14

14

-1.0

50

0.2

93

SW

AP

TIO

N-0

.909

0.1

34

-6.8

00

0.0

00

3.0

66

0.2

50

12.2

70

0.0

00

sh

ort

-term

eq

uati

on

ad

just

men

t p

ara

mer

ter（

ϕi）

-0.0

05

0.0

01

-7.9

00

0.0

00

86.9

3（

0.0

001）

-0.0

12

0.0

01

-9.7

00

0.0

00

449.7

0(0

.0000)

⊿L

EV

ER

AG

E35

19

1.8

70

0.0

61

136.6

4(0

.0000)

150

73

2.0

50

0.0

40

211.0

8(0

.0000)

⊿V

OL

AT

ILIT

Y3.3

70

1.3

25

2.5

40

0.0

11

164.6

1(0

.0000)

44

29

1.5

00

0.1

33

161.7

5(0

.0000)

⊿R

F97

90

1.0

80

0.2

81

32.3

3(0

.9035)

-336

242

-1.3

90

0.1

64

24.9

7(

0.9

907)

⊿S

QR

(RF

)(i

i)-8

.202

8.7

97

-0.9

30

0.3

51

26.6

4(0

.9820)

-104

31

-3.3

40

0.0

01

18.9

8(0

.9996)

⊿S

WA

PT

ION

0.0

07

0.0

02

3.2

10

0.0

01

23.3

9(0

.9955)

-0.0

23

0.0

34

-0.6

60

0.5

06

51.0

9(0

.2150)

⊿V

IX0.0

06

0.0

14

0.4

50

0.6

56

31.8

6(

0.9

138)

0.1

82

0.0

49

3.7

30

0.0

00

83.5

5(0

.0003)

log

lik

elih

oo

d

ad

j-R

2

ob

s

Befo

re t

he c

risis

(P

MG

)A

fter

the c

risis

(P

MG

)

-18,5

02

-63,3

41

0.0

70.2

4

33,3

90

23,1

74


- 36 -

Table 9 (continued)

Pan

el B

: d

ep

en

den

t v

ari

ab

le＝

⊿ln

(CD

SS

)

co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)(i

)co

ef

s.e

.z-

valu

ep

-valu

eχ

2(p

-valu

e)(i

)

lon

g-t

erm

eq

uati

on

LE

VE

RA

GE

2.8

17

2.5

91

1.0

90

0.2

77

2.2

51

0.8

32

2.7

10

0.0

07

VO

LA

TIL

ITY

0.2

82

0.4

85

0.5

80

0.5

61

0.4

39

0.1

40

3.1

30

0.0

02

RF

-353

257

-1.3

70

0.1

70

-2,9

02

161

-18

0.0

00

SQ

R(R

F)

(ii)

0.1

82

0.8

53

0.2

10

0.8

31

9.2

64

0.5

25

18

0.0

00

TS

467

75

6.1

90

0.0

00

-145

16

-8.8

90

0.0

00

TO

PIX

3.3

59

4.1

29

0.8

10

0.4

16

-15

1.2

59

-12

0.0

00

ln(M

V)

-1.0

52

0.3

48

-3.0

30

0.0

02

-0.9

55

0.1

52

-60.0

00

SW

AP

TIO

N-0

.082

0.0

15

-5.3

80

0.0

00

0.0

52

0.0

02

22

0.0

00

sh

ort

-term

eq

uati

on

adju

stm

ent

para

mer

ter（

ϕi）

-0.0

03

0.0

00

-16

0.0

00

22.3

5(0

.9973)

-0.0

16

0.0

01

-23

0.0

00

147.1

7(0

.0000)

⊿L

EV

ER

AG

E0.8

34

0.1

46

5.7

00

0.0

00

184.6

1(0

.0000)

0.2

65

0.1

49

1.7

80

0.0

76

100.8

6(0

.0000)

⊿V

OL

AT

ILIT

Y0.2

47

0.0

32

7.6

00

0.0

00

185.6

0(0

.0000)

0.1

20

0.0

33

3.6

00

0.0

00

95.9

4(0

.0000)

⊿R

F0.8

90

0.4

39

2.0

30

0.0

43

29.2

9(0

.9567)

-8.7

94

0.8

39

-10

0.0

00

46.6

0(0

.3661)

⊿S

QR

(RF

)(i

i)-0

.001

0.0

96

-0.0

10

0.9

94

29.4

9(0

.9542)

-0.4

21

0.1

24

-3.4

00

0.0

01

28.2

0(0

.9692)

⊿S

WA

PT

ION

0.0

00

0.0

00

7.0

00

0.0

00

21.5

5(0

.9982)

0.0

00

0.0

00

-0.6

10

0.5

44

40.5

4(0

.6208)

⊿V

IX0.0

01

0.0

00

6.6

60

0.0

00

34.2

9(0

.8533)

0.0

01

0.0

00

19

0.0

00

25.2

5(0

.9896)

log

lik

elih

oo

d

ad

j-R

2

ob

s33,3

90

23,1

74

83,8

46

45,2

68

0.0

50.1

2

Befo

re t

he c

risis

(P

MG

)A

fter

the c

risis

(P

MG

)


- 37 -

Table 10: Principal Component Analysis

Figures are the contributions of principal components.

Before the Crisis After the crisis Before the Crisis After the crisis

1st principa component 38.0% 45.8% 38.5% 38.9%

2nd principal component 6.3% 7.8% 6.2% 7.3%

3rd principal component 5.2% 5.4% 4.8% 6.4%

4th principal component 4.0% 3.9% 4.0% 4.7%


Before the Crisis After the crisis Before the Crisis After the crisis

1st principa component 35.5% 58.4% 36.0% 50.2%

2nd principal component 6.9% 5.0% 6.8% 5.5%

3rd principal component 5.1% 4.3% 4.7% 5.0%



⊿ ln(CDSS)

raw variable residuals from full model

⊿ CDSS

raw variable residuals from full model

Figure 1: Scatter Plot of Eigenvectors of 1st Principal Components

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.00 0.05 0.10 0.15 0.20

before the crisis

after the crisis

(eigenvector of 1st principal component, using ⊿ln(CDSS)

(eig

en

vecto

r of

1st p

rincip

al c

om

po

nen

t, usin

gre

sidu

al o

f full m

od

el)

Financial Research Center （FSA Institute）

Financial Services Agency

Government of Japan

3-2-1 Kasumigaseki, Chiyoda-ku, Tokyo 100-8967, Japan

TEL：03-3506-6000（ext 3293）

FAX：03-3506-6716

URL：http://www.fsa.go.jp/frtc/english/index.html

http://www.fsa.go.jp/frtc/english/index.html

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